A selective review of statistical methods using calibration information from similar studies

Abstract

In the era of big data, divide-and-conquer, parallel, and distributed inference methods have become increasingly popular. How to effectively use the calibration information from each machine in parallel computation has become a challenging task for statisticians and computer scientists. Many newly developed methods have roots in traditional statistical approaches that make use of calibration information. In this paper, we first review some classical statistical methods for using calibration information, including simple meta-analysis methods, parametric likelihood, empirical likelihood, and the generalized method of moments. We further investigate how these methods incorporate summarized or auxiliary information from previous studies, related studies, or populations. We find that the methods based on summarized data usually have little or nearly no efficiency loss compared with the corresponding methods based on all-individual data. Finally, we review some recently developed big data analysis methods including communication-efficient distributed approaches, renewal estimation, and incremental inference as examples of the latest developments in methods using calibration information.

Keywords:

• Calibration information
• empirical likelihood
• estimating equations
• generalized method of moments
• meta-analysis

Acknowledgments

The authors thank the editor and two referees for constructive comments and suggestions that led to significant improvements in this paper.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 71931004, 12171157, and 32030063], the 111 Project [grant number B14019], the Development Fund for Shanghai Talents and the Natural Sciences and Engineering Research Council of Canada (grant number RGPIN-2020-04964).